Download Grade 6 - Willingboro School

SUMMER MATH PACKET
Grade 6
t+
Summer Packet - 5th into 6th grade
Name
Addition
1
1
Find thesum of the two numbers in each problem.
Show all work.
4
Example:
4
8
+ 18 8
6
1.
652
2.
+ 345
203
3.
+ 525
3 6
726
+ 268
Decimal Addition:
Remember to line up the decimals before adding. Bring the decimal straight down in your answer.
4.
7.75
5.
51.4 + 2.86
6.
.1274 + 8.25
+ 1.46
3
13
Subtraction
7
St
2
Find the difference between the two numbers in
each problem. Show all work.
2
1
8
5
2
5
7.
Example:
8.
407
7,007
3,414
- 198
-2,426
-1.218
Decimal Subtraction*.
Remember to line up the decimals before subtracting. Bring the decimal straight down in your
answer.
10.
11.
338.38
-
149.27
12.
80.401 - 44.23
75.89 - 9.4
54
Example:
Multiplication
Find the product of the two numbers in each
x!6
324
problem. Show all work.
+ 540
864
13.
14.
15.
65
x
42
4
x
84
8
x
39
Decimal Multiplication:
Multiply as you would with whole numbers. Count the decimal places in each factor. The product
(answer) has the same number of decimal places.
16.
17.
.13
x
18.
5.1
70
.108
2
x
2.5
Division
Find the quotient in each problem. If there is aremainder, state the
reminders as R=_. show all work. Feel free to use aseparate sheet of
paper.
19.
20.
7J591
21.
12)264
43)2815
J
Decimal Division:
If the divisor (outside number) is adecimal, you must move the decimal point (using multiplication)
to the right until it becomes awhole number. Then, move the decimal in the dividend (inside
number) the same number of times. Divide to find your answer (quotient).
Then, move the decimal straight up from the dividend to the quotient.
quotient
divisor) dividend
Remember, no remainders.
22.
23.
3J3L8
24.
.5]lA5
,12)12.24
Rounding
Underline the given place value. Look to the right. If this digit is
5 or greater, increase the underlined digit by 1. If the digit to
Round to the
nearest...
the right is less than 5, keep the underlined digit thesame.
hundredth
0.547
0.55
Round to the nearest.
25
tenth
26. hundredth
0.3479
28
ten
27. whole number
0.7553
29.
162.21
thousandth
3.268
30.
0.0036
hundred
990.54
Compare using <, >, or =
1.2 O 1.20
Compare the decimals.
31. 0.205 O 0.21
32. 1.03
34.
35. 0.52 Q 0.500
0.1 Q 0.1000
Oa 03
1.2 =1.20
33. 0.04 O
0.050
36. 0.41 (^) 0.405
Prime Number: Awhole number greater than 1that has only two factors 1and itself
Examples: 2, 3, 5, 7,11,13,17, and 19 are all prime numbers.
Composite Number: Awhole number greater than 1that has more than two factors.
Example: 8is acomposite number since its factors are 1, 2,4, 8.
Determine if the following numbers are prime or composite. If the numbers are composite,
please list all of the factors.
37.
27:
38.
39:
39.
43:
40.
49:
Exponents
ImL 2TT1 mUJt'^ation *the*™ **tor *to use an exponent. In this
exampk. 2=2x2x2 =8. The small raised three is the exponent. It tells how
many t.mes the number 2, called the base, is multiplied by itself
ftdth^value0""9 eXPreSSi0nS ^ Wr'nin9 ^ eXpanded notatio" ^«* multiplication) and
4L
6'
4244. eight squared
26
43.
^
3<
fjvecubed
Greatest Common Factor
The greatest factor that two or more numbers
have in common (GCF).
1. List all the factors of four in order
2. List all the factors of twenty in order
3. List the common factors
Finding Common Factors:
4: 1. 2, 4
20: 1, 2, 4, 5, 10, 20
Common Factors: 1, 2, 4
GCF- 4
4. Write the greatest common factor
List all the factors for each number. Circle the common factors.
46.
18:
30:
Common Factors:
47.
Greatest Common Factor:
60:
45:
Common Factors:
48.
Greatest Common Factor:
23:
29:
Common Factors:
49.
Greatest Common Factor:
56:
72:
Common Factors:
Greatest Common Factor:
Least Common Multiple
The smallest nonzero multiple that two or more
numbers have in common.
1. List the first 6 multiples of 4
2. List the first 6 multiples of 6
3. List the common multiples
Finding Common Multiples:
4: 4, 8, 12, 16, 20, 24
6: 6, 12, 18, 24, 30, 36
Least Common Multiple= 12
4. Write the least common multiple.
50.
8:
12:
Common Multiples:
51.
Least Common Multiple:
7:.
11:
Common Multiples:
52.
_Least Common Multiple:
25:
10:
Common Multiples:
53.
Least Common Multiple:
24:
36:
Common Multiples:
Least Common Multiple:
Prime Factorization is a composite number
renamed as a product of prime numbers. You
may make a factor tree to find the answer. Put
final answer in exponent form.
Find the prime factorization of 36.
36
/
/ \
2x3
54.
56.
\
6x6
/\
2x3
55.
57.
48
22x32
Comparing Fractions
Compare each pair of numbers. Write the
correct comparison symbol (<,>, = ) in each
circle. Make sure you have common
Example:
1
o
3
denominators before comparing numerators.
3
4
1
I
4
9
12
58.
59.
iO I
61.
60.
iOi
iOJ
62.
i o
i
12
63.
10
tCH
Ordering Fractions
Order the following fractions from least to greatest.
64.
65.
10
_6_
_7_
10
10
66.
67.
2
_5_
30
_9_
16
64
32
Order of Operations
Solve the following problems. Show your work. Be
sure to follow the order of operations.
Parenthesis
Exponents
Multiplication or Division: Which ever comes first
from left to right.
Addition or Subtraction: Which ever comes first
from left to right.
Example:
8-4-2+2=
8-2+2=
6 + 2 =
8
68.
15 x 8 - 3 =
69.
36 4-4x3 =
71.
(30 +8) x (6-1) =
72.
(29-18) +144. 2+ 6=
74.
36 - 5 (16 -11) =
75.
25 + 18 * 6 - 1 =
70.
(30 +8) x 6 -1 =
73. 64-8x2
76.
24 + 62-l4
=
10
Geometry-Who am I?
Use the following shapes to answer the
questions below.
77 Ian «12 dimensional shape ,hat has four sides. Iha»e four 90 degree anoles Iha»e
Who am I?
Jii".hLt^'s-S",°*te""*—anste *" °f *> —-*•—
Who am I?
79 Iam a2dimensional shape that has four sides. I have two obtuse anoles and two
one length, and my other two sides are adifferent length.
Who am I?
11?
si that are
any sides
paralle °2d,'menS,'0na, Shape that hQS 5**« -S««. Ido not have any
Who am I?
are allThe"sVmeTngt'l&
f°Ur 9°sets^of parallel
"^lines.rhaVe *" ^ that
me same length. I have tw
two^different
Who am I?
82. Iam a2dimensional shape. My perimeter is also known as a circumference.
Who am I?
11
Simply Fractions
Simplify the following fractions. If the fractions
are improper, change them to mixed numbers
then simplify.
83.
Example:
10*5= 2
25*5=
84.
5
85.
11
11
12
28
55
51
86.
87.
88.
34
17
80
48
4
25
Adding Fractions and Mixed Numbers
Add the following fractions. Makesure
Example:
you have common denominators before adding.
Remember, you only add the numerator (top
1
number) and you keep the denominator (bottom
number) the same! Simplify your final answers.
1
i i
_5_+_3_ __
8
15 15 ~15
89.
90.
10*10
91.
92.
3
2
i+_5 _
8
8
9+6 "
2- +1-
-Ui!
12
3
12
Subtracting Fractions
Subtract the following fractions. Make
Example:
sure you have common denominators before
subtracting. Remember, you only subtract the
numerator (top number) and you keep the
ii
denominator (bottom number) the same!
5
Simplify your final answers.
93.
2
6~ 6
94.
95.
5_3
6~6
12
96.
1_ 2
10 ~4
12
3±-I
5
4
Multiplying Fractions
Multiply the following fractions. Multiply
the numerators; then multiply the denominators.
Simplify, if necessary.
97.
98.
3
1
-x- =
4
3
Example:
3
5X 9" 45 ' 3
99.
2
5
-X- =
3
8
5_]5_J_
100.
1
2
-X- =
3
5
1x2
8